Real time wave vector filtering in one-dimensional media.

Abstract

Often it is necessary to measure the wave vector components of propagating waves in vibrating media. Some examples are: measurement of traveling flexural and extensional waves in beams; measurement of acoustic waves in ducts; and determination of boundary conditions in structural or acoustic systems. In previous work, a time domain technique for wave vector filtering of plane waves in ducts was developed which required that the sensor spacing relative to the wavelength of interest be small. Frequency domain techniques have also been developed to perform wave vector filtering in both dispersive and nondispersive media. These techniques cannot be used in real time because of the signal processing requirements. In this work, a new time domain technique is presented that utilizes two sensor locations in conjunction with a digital filter, for each wave type, to provide a real time estimate of the complex amplitude of each of the traveling wave components for both dispersive and nondispersive media. The technique estimates the wave components over a band-limited spectra whose limits are dictated by the spacing between the sensors (up to a spacing of half a wavelength). A simulation is used to determine the performance of the new technique in both dispersive and nondispersive media over a range of frequencies.